Abstract

We present a conceptual demonstration of a metallic planar lens composed of double-turn waveguides for sub-diffraction-limit focusing. The phase delay of a single double-turn waveguide dependent on its structural parameters is investigated by employing the finite-difference time-domain (FDTD) numerical method. The design utilizes the surface plasmon polaritons (SPPs) that propagate along the metal-insulator-metal (MIM) waveguides to achieve the desired spatial phase modulation in the transmitted field. The simulated focal length achieved is in positive agreement with the design and the full-width at half-maximum (FWHM) is 0.446λ, well beyond the diffraction limit. This superfocusing performance can be maintained very well under the slight change of film thickness and slit width, showing the robustness of the design. The maximum aspect ratio of nanoslits constructing the proposed lens is 3.33, which is far less than the previous reports, alleviating the later fabrication. The metallic planar lens as demonstrated will find its applications in such fields as lithography, integrated optics, and super-resolution imaging.

© 2017 Optical Society of America

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References

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  1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
    [Crossref] [PubMed]
  2. Y. Yu and H. Zappe, “Effect of lens size on the focusing performance of plasmonic lenses and suggestions for the design,” Opt. Express 19(10), 9434–9444 (2011).
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    [Crossref] [PubMed]
  4. H. Shao, J. Wang, D. Liu, Z.-D. Hu, X. Xia, and T. Sang, “Plasmonic planar lens based on slanted nanoslit array,” Plasmonics 12(2), 361–367 (2017).
    [Crossref]
  5. H. Gao, J. K. Hyun, M. H. Lee, J.-C. Yang, L. J. Lauhon, and T. W. Odom, “Broadband plasmonic microlenses based on patches of nanoholes,” Nano Lett. 10(10), 4111–4116 (2010).
    [Crossref] [PubMed]
  6. Z. Shi, Y. Fu, X. Zhou, and S. Zhu, “Polarization effect on superfocusing of a plasmonic lens structured with radialized and chirped elliptical nanopinholes,” Plasmonics 5(2), 175–182 (2010).
    [Crossref]
  7. J. Qi, T. Kaiser, A. E. Klein, M. Steinert, T. Pertsch, F. Lederer, and C. Rockstuhl, “Enhancing resonances of optical nanoantennas by circular gratings,” Opt. Express 23(11), 14583–14595 (2015).
    [Crossref] [PubMed]
  8. J. Ji, Y. Meng, L. Sun, X. Wu, and J. Wang, “Strong focusing of plasmonic lens with nanofinger and multiple concentric rings under radially polarized illumination,” Plasmonics 11(1), 23–27 (2016).
    [Crossref]
  9. X. Ni, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin, planar, Babinet-inverted plasmonic metalenses,” Light Sci. Appl. 2(4), e72 (2013).
    [Crossref]
  10. L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, “Plasmonic lenses formed by two-dimensional nanometric cross-shaped aperture arrays for Fresnel-region focusing,” Nano Lett. 10(5), 1936–1940 (2010).
    [Crossref] [PubMed]
  11. Y. Gao, J. Liu, K. Guo, Y. Gao, and S. Liu, “A side-illuminated plasmonic planar lens,” Opt. Express 22(1), 699–706 (2014).
    [Crossref] [PubMed]
  12. B. Jia, H. Shi, J. Li, Y. Fu, C. Du, and M. Gu, “Near-field visualization of focal depth modulation by step corrugated plasmonic slits,” Appl. Phys. Lett. 94(15), 151912 (2009).
    [Crossref]
  13. Y. Yu and H. Zappe, “Theory and implementation of focal shift of plasmonic lenses,” Opt. Lett. 37(9), 1592–1594 (2012).
    [Crossref] [PubMed]
  14. Y. Zhu, W. Yuan, Y. Yu, and P. Wang, “Robustly efficient superfocusing of immersion plasmonic lenses based on coupled nanoslits,” Plasmonics 11(6), 1543–1548 (2016).
    [Crossref]
  15. L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  17. L. Chen, Y. Wei, X. Zang, Y. Zhu, and S. Zhuang, “Excitation of dark multipolar plasmonic resonances at terahertz frequencies,” Sci. Rep. 6(1), 22027 (2016).
    [Crossref] [PubMed]
  18. Z. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano-optic lenses,” Appl. Phys. Lett. 85(4), 642–644 (2004).
    [Crossref]
  19. H. Shi, C. Wang, C. Du, X. Luo, X. Dong, and H. Gao, “Beam manipulating by metallic nano-slits with variant widths,” Opt. Express 13(18), 6815–6820 (2005).
    [Crossref] [PubMed]
  20. J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006).
    [Crossref]
  21. W. L. Barnes, “Surface plasmon–polariton length scales: a route to sub-wavelength optics,” J. Opt. A, Pure Appl. Opt. 8(4), S87–S93 (2006).
    [Crossref]
  22. K. Huang, H. Ye, J. Teng, S. P. Yeo, B. Luk’yanchuk, and C.-W. Qiu, “Optimization-free superoscillatory lens using phase and amplitude masks,” Laser Photonics Rev. 8(1), 152–157 (2014).
    [Crossref]

2017 (1)

H. Shao, J. Wang, D. Liu, Z.-D. Hu, X. Xia, and T. Sang, “Plasmonic planar lens based on slanted nanoslit array,” Plasmonics 12(2), 361–367 (2017).
[Crossref]

2016 (3)

Y. Zhu, W. Yuan, Y. Yu, and P. Wang, “Robustly efficient superfocusing of immersion plasmonic lenses based on coupled nanoslits,” Plasmonics 11(6), 1543–1548 (2016).
[Crossref]

J. Ji, Y. Meng, L. Sun, X. Wu, and J. Wang, “Strong focusing of plasmonic lens with nanofinger and multiple concentric rings under radially polarized illumination,” Plasmonics 11(1), 23–27 (2016).
[Crossref]

L. Chen, Y. Wei, X. Zang, Y. Zhu, and S. Zhuang, “Excitation of dark multipolar plasmonic resonances at terahertz frequencies,” Sci. Rep. 6(1), 22027 (2016).
[Crossref] [PubMed]

2015 (2)

2014 (2)

Y. Gao, J. Liu, K. Guo, Y. Gao, and S. Liu, “A side-illuminated plasmonic planar lens,” Opt. Express 22(1), 699–706 (2014).
[Crossref] [PubMed]

K. Huang, H. Ye, J. Teng, S. P. Yeo, B. Luk’yanchuk, and C.-W. Qiu, “Optimization-free superoscillatory lens using phase and amplitude masks,” Laser Photonics Rev. 8(1), 152–157 (2014).
[Crossref]

2013 (1)

X. Ni, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin, planar, Babinet-inverted plasmonic metalenses,” Light Sci. Appl. 2(4), e72 (2013).
[Crossref]

2012 (1)

2011 (1)

2010 (4)

L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, “Plasmonic lenses formed by two-dimensional nanometric cross-shaped aperture arrays for Fresnel-region focusing,” Nano Lett. 10(5), 1936–1940 (2010).
[Crossref] [PubMed]

H. Gao, J. K. Hyun, M. H. Lee, J.-C. Yang, L. J. Lauhon, and T. W. Odom, “Broadband plasmonic microlenses based on patches of nanoholes,” Nano Lett. 10(10), 4111–4116 (2010).
[Crossref] [PubMed]

Z. Shi, Y. Fu, X. Zhou, and S. Zhu, “Polarization effect on superfocusing of a plasmonic lens structured with radialized and chirped elliptical nanopinholes,” Plasmonics 5(2), 175–182 (2010).
[Crossref]

Q. Chen and D. R. S. Cumming, “Visible light focusing demonstrated by plasmonic lenses based on nano-slits in an aluminum film,” Opt. Express 18(14), 14788–14793 (2010).
[Crossref] [PubMed]

2009 (2)

B. Jia, H. Shi, J. Li, Y. Fu, C. Du, and M. Gu, “Near-field visualization of focal depth modulation by step corrugated plasmonic slits,” Appl. Phys. Lett. 94(15), 151912 (2009).
[Crossref]

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[Crossref] [PubMed]

2006 (2)

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006).
[Crossref]

W. L. Barnes, “Surface plasmon–polariton length scales: a route to sub-wavelength optics,” J. Opt. A, Pure Appl. Opt. 8(4), S87–S93 (2006).
[Crossref]

2005 (1)

2004 (1)

Z. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano-optic lenses,” Appl. Phys. Lett. 85(4), 642–644 (2004).
[Crossref]

2003 (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

Atwater, H. A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006).
[Crossref]

Barnard, E. S.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[Crossref] [PubMed]

Barnes, W. L.

W. L. Barnes, “Surface plasmon–polariton length scales: a route to sub-wavelength optics,” J. Opt. A, Pure Appl. Opt. 8(4), S87–S93 (2006).
[Crossref]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

Brongersma, M. L.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[Crossref] [PubMed]

Catrysse, P. B.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[Crossref] [PubMed]

Chen, L.

L. Chen, Y. Wei, X. Zang, Y. Zhu, and S. Zhuang, “Excitation of dark multipolar plasmonic resonances at terahertz frequencies,” Sci. Rep. 6(1), 22027 (2016).
[Crossref] [PubMed]

Chen, Q.

Cumming, D. R. S.

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

Diao, J.

Dionne, J. A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006).
[Crossref]

Dong, X.

Du, C.

B. Jia, H. Shi, J. Li, Y. Fu, C. Du, and M. Gu, “Near-field visualization of focal depth modulation by step corrugated plasmonic slits,” Appl. Phys. Lett. 94(15), 151912 (2009).
[Crossref]

H. Shi, C. Wang, C. Du, X. Luo, X. Dong, and H. Gao, “Beam manipulating by metallic nano-slits with variant widths,” Opt. Express 13(18), 6815–6820 (2005).
[Crossref] [PubMed]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

Fan, S.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[Crossref] [PubMed]

Fu, Y.

Z. Shi, Y. Fu, X. Zhou, and S. Zhu, “Polarization effect on superfocusing of a plasmonic lens structured with radialized and chirped elliptical nanopinholes,” Plasmonics 5(2), 175–182 (2010).
[Crossref]

B. Jia, H. Shi, J. Li, Y. Fu, C. Du, and M. Gu, “Near-field visualization of focal depth modulation by step corrugated plasmonic slits,” Appl. Phys. Lett. 94(15), 151912 (2009).
[Crossref]

Gao, H.

H. Gao, J. K. Hyun, M. H. Lee, J.-C. Yang, L. J. Lauhon, and T. W. Odom, “Broadband plasmonic microlenses based on patches of nanoholes,” Nano Lett. 10(10), 4111–4116 (2010).
[Crossref] [PubMed]

H. Shi, C. Wang, C. Du, X. Luo, X. Dong, and H. Gao, “Beam manipulating by metallic nano-slits with variant widths,” Opt. Express 13(18), 6815–6820 (2005).
[Crossref] [PubMed]

Gao, Y.

Goh, X. M.

L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, “Plasmonic lenses formed by two-dimensional nanometric cross-shaped aperture arrays for Fresnel-region focusing,” Nano Lett. 10(5), 1936–1940 (2010).
[Crossref] [PubMed]

Gu, M.

B. Jia, H. Shi, J. Li, Y. Fu, C. Du, and M. Gu, “Near-field visualization of focal depth modulation by step corrugated plasmonic slits,” Appl. Phys. Lett. 94(15), 151912 (2009).
[Crossref]

Guo, K.

Hu, Z.-D.

H. Shao, J. Wang, D. Liu, Z.-D. Hu, X. Xia, and T. Sang, “Plasmonic planar lens based on slanted nanoslit array,” Plasmonics 12(2), 361–367 (2017).
[Crossref]

Huang, K.

K. Huang, H. Ye, J. Teng, S. P. Yeo, B. Luk’yanchuk, and C.-W. Qiu, “Optimization-free superoscillatory lens using phase and amplitude masks,” Laser Photonics Rev. 8(1), 152–157 (2014).
[Crossref]

Hyun, J. K.

H. Gao, J. K. Hyun, M. H. Lee, J.-C. Yang, L. J. Lauhon, and T. W. Odom, “Broadband plasmonic microlenses based on patches of nanoholes,” Nano Lett. 10(10), 4111–4116 (2010).
[Crossref] [PubMed]

Ishii, S.

X. Ni, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin, planar, Babinet-inverted plasmonic metalenses,” Light Sci. Appl. 2(4), e72 (2013).
[Crossref]

Ji, J.

J. Ji, Y. Meng, L. Sun, X. Wu, and J. Wang, “Strong focusing of plasmonic lens with nanofinger and multiple concentric rings under radially polarized illumination,” Plasmonics 11(1), 23–27 (2016).
[Crossref]

Jia, B.

B. Jia, H. Shi, J. Li, Y. Fu, C. Du, and M. Gu, “Near-field visualization of focal depth modulation by step corrugated plasmonic slits,” Appl. Phys. Lett. 94(15), 151912 (2009).
[Crossref]

Kaiser, T.

Kildishev, A. V.

X. Ni, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin, planar, Babinet-inverted plasmonic metalenses,” Light Sci. Appl. 2(4), e72 (2013).
[Crossref]

Kim, H. K.

Z. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano-optic lenses,” Appl. Phys. Lett. 85(4), 642–644 (2004).
[Crossref]

Klein, A. E.

Lauhon, L. J.

H. Gao, J. K. Hyun, M. H. Lee, J.-C. Yang, L. J. Lauhon, and T. W. Odom, “Broadband plasmonic microlenses based on patches of nanoholes,” Nano Lett. 10(10), 4111–4116 (2010).
[Crossref] [PubMed]

Lederer, F.

Lee, M. H.

H. Gao, J. K. Hyun, M. H. Lee, J.-C. Yang, L. J. Lauhon, and T. W. Odom, “Broadband plasmonic microlenses based on patches of nanoholes,” Nano Lett. 10(10), 4111–4116 (2010).
[Crossref] [PubMed]

Li, J.

B. Jia, H. Shi, J. Li, Y. Fu, C. Du, and M. Gu, “Near-field visualization of focal depth modulation by step corrugated plasmonic slits,” Appl. Phys. Lett. 94(15), 151912 (2009).
[Crossref]

Lin, L.

L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, “Plasmonic lenses formed by two-dimensional nanometric cross-shaped aperture arrays for Fresnel-region focusing,” Nano Lett. 10(5), 1936–1940 (2010).
[Crossref] [PubMed]

Liu, D.

H. Shao, J. Wang, D. Liu, Z.-D. Hu, X. Xia, and T. Sang, “Plasmonic planar lens based on slanted nanoslit array,” Plasmonics 12(2), 361–367 (2017).
[Crossref]

Liu, J.

Liu, S.

Luk’yanchuk, B.

K. Huang, H. Ye, J. Teng, S. P. Yeo, B. Luk’yanchuk, and C.-W. Qiu, “Optimization-free superoscillatory lens using phase and amplitude masks,” Laser Photonics Rev. 8(1), 152–157 (2014).
[Crossref]

Luo, X.

McGuinness, L. P.

L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, “Plasmonic lenses formed by two-dimensional nanometric cross-shaped aperture arrays for Fresnel-region focusing,” Nano Lett. 10(5), 1936–1940 (2010).
[Crossref] [PubMed]

Meng, Y.

J. Ji, Y. Meng, L. Sun, X. Wu, and J. Wang, “Strong focusing of plasmonic lens with nanofinger and multiple concentric rings under radially polarized illumination,” Plasmonics 11(1), 23–27 (2016).
[Crossref]

Ni, X.

X. Ni, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin, planar, Babinet-inverted plasmonic metalenses,” Light Sci. Appl. 2(4), e72 (2013).
[Crossref]

Odom, T. W.

H. Gao, J. K. Hyun, M. H. Lee, J.-C. Yang, L. J. Lauhon, and T. W. Odom, “Broadband plasmonic microlenses based on patches of nanoholes,” Nano Lett. 10(10), 4111–4116 (2010).
[Crossref] [PubMed]

Pertsch, T.

Polman, A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006).
[Crossref]

Qi, J.

Qiu, C.-W.

K. Huang, H. Ye, J. Teng, S. P. Yeo, B. Luk’yanchuk, and C.-W. Qiu, “Optimization-free superoscillatory lens using phase and amplitude masks,” Laser Photonics Rev. 8(1), 152–157 (2014).
[Crossref]

Roberts, A.

L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, “Plasmonic lenses formed by two-dimensional nanometric cross-shaped aperture arrays for Fresnel-region focusing,” Nano Lett. 10(5), 1936–1940 (2010).
[Crossref] [PubMed]

Rockstuhl, C.

Sang, T.

H. Shao, J. Wang, D. Liu, Z.-D. Hu, X. Xia, and T. Sang, “Plasmonic planar lens based on slanted nanoslit array,” Plasmonics 12(2), 361–367 (2017).
[Crossref]

Shalaev, V. M.

X. Ni, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin, planar, Babinet-inverted plasmonic metalenses,” Light Sci. Appl. 2(4), e72 (2013).
[Crossref]

Shao, H.

H. Shao, J. Wang, D. Liu, Z.-D. Hu, X. Xia, and T. Sang, “Plasmonic planar lens based on slanted nanoslit array,” Plasmonics 12(2), 361–367 (2017).
[Crossref]

Shi, H.

B. Jia, H. Shi, J. Li, Y. Fu, C. Du, and M. Gu, “Near-field visualization of focal depth modulation by step corrugated plasmonic slits,” Appl. Phys. Lett. 94(15), 151912 (2009).
[Crossref]

H. Shi, C. Wang, C. Du, X. Luo, X. Dong, and H. Gao, “Beam manipulating by metallic nano-slits with variant widths,” Opt. Express 13(18), 6815–6820 (2005).
[Crossref] [PubMed]

Shi, Z.

Z. Shi, Y. Fu, X. Zhou, and S. Zhu, “Polarization effect on superfocusing of a plasmonic lens structured with radialized and chirped elliptical nanopinholes,” Plasmonics 5(2), 175–182 (2010).
[Crossref]

Steinert, M.

Sun, L.

J. Ji, Y. Meng, L. Sun, X. Wu, and J. Wang, “Strong focusing of plasmonic lens with nanofinger and multiple concentric rings under radially polarized illumination,” Plasmonics 11(1), 23–27 (2016).
[Crossref]

Sun, Z.

Z. Sun and H. K. Kim, “Refractive transmission of light and beam shaping with metallic nano-optic lenses,” Appl. Phys. Lett. 85(4), 642–644 (2004).
[Crossref]

Sweatlock, L. A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006).
[Crossref]

Teng, J.

K. Huang, H. Ye, J. Teng, S. P. Yeo, B. Luk’yanchuk, and C.-W. Qiu, “Optimization-free superoscillatory lens using phase and amplitude masks,” Laser Photonics Rev. 8(1), 152–157 (2014).
[Crossref]

Verslegers, L.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[Crossref] [PubMed]

Wang, C.

Wang, J.

H. Shao, J. Wang, D. Liu, Z.-D. Hu, X. Xia, and T. Sang, “Plasmonic planar lens based on slanted nanoslit array,” Plasmonics 12(2), 361–367 (2017).
[Crossref]

J. Ji, Y. Meng, L. Sun, X. Wu, and J. Wang, “Strong focusing of plasmonic lens with nanofinger and multiple concentric rings under radially polarized illumination,” Plasmonics 11(1), 23–27 (2016).
[Crossref]

Wang, P.

Y. Zhu, W. Yuan, Y. Yu, and P. Wang, “Robustly efficient superfocusing of immersion plasmonic lenses based on coupled nanoslits,” Plasmonics 11(6), 1543–1548 (2016).
[Crossref]

Wei, Y.

L. Chen, Y. Wei, X. Zang, Y. Zhu, and S. Zhuang, “Excitation of dark multipolar plasmonic resonances at terahertz frequencies,” Sci. Rep. 6(1), 22027 (2016).
[Crossref] [PubMed]

White, J. S.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[Crossref] [PubMed]

Wu, X.

J. Ji, Y. Meng, L. Sun, X. Wu, and J. Wang, “Strong focusing of plasmonic lens with nanofinger and multiple concentric rings under radially polarized illumination,” Plasmonics 11(1), 23–27 (2016).
[Crossref]

Xia, X.

H. Shao, J. Wang, D. Liu, Z.-D. Hu, X. Xia, and T. Sang, “Plasmonic planar lens based on slanted nanoslit array,” Plasmonics 12(2), 361–367 (2017).
[Crossref]

Yang, J.-C.

H. Gao, J. K. Hyun, M. H. Lee, J.-C. Yang, L. J. Lauhon, and T. W. Odom, “Broadband plasmonic microlenses based on patches of nanoholes,” Nano Lett. 10(10), 4111–4116 (2010).
[Crossref] [PubMed]

Ye, H.

K. Huang, H. Ye, J. Teng, S. P. Yeo, B. Luk’yanchuk, and C.-W. Qiu, “Optimization-free superoscillatory lens using phase and amplitude masks,” Laser Photonics Rev. 8(1), 152–157 (2014).
[Crossref]

Yeo, S. P.

K. Huang, H. Ye, J. Teng, S. P. Yeo, B. Luk’yanchuk, and C.-W. Qiu, “Optimization-free superoscillatory lens using phase and amplitude masks,” Laser Photonics Rev. 8(1), 152–157 (2014).
[Crossref]

Yu, Y.

Yu, Z.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[Crossref] [PubMed]

Yuan, W.

Y. Zhu, W. Yuan, Y. Yu, and P. Wang, “Robustly efficient superfocusing of immersion plasmonic lenses based on coupled nanoslits,” Plasmonics 11(6), 1543–1548 (2016).
[Crossref]

Y. Zhu, W. Yuan, Y. Yu, and J. Diao, “Metallic planar lens formed by coupled width-variable nanoslits for superfocusing,” Opt. Express 23(15), 20124–20131 (2015).
[Crossref] [PubMed]

Zang, X.

L. Chen, Y. Wei, X. Zang, Y. Zhu, and S. Zhuang, “Excitation of dark multipolar plasmonic resonances at terahertz frequencies,” Sci. Rep. 6(1), 22027 (2016).
[Crossref] [PubMed]

Zappe, H.

Zhou, X.

Z. Shi, Y. Fu, X. Zhou, and S. Zhu, “Polarization effect on superfocusing of a plasmonic lens structured with radialized and chirped elliptical nanopinholes,” Plasmonics 5(2), 175–182 (2010).
[Crossref]

Zhu, S.

Z. Shi, Y. Fu, X. Zhou, and S. Zhu, “Polarization effect on superfocusing of a plasmonic lens structured with radialized and chirped elliptical nanopinholes,” Plasmonics 5(2), 175–182 (2010).
[Crossref]

Zhu, Y.

L. Chen, Y. Wei, X. Zang, Y. Zhu, and S. Zhuang, “Excitation of dark multipolar plasmonic resonances at terahertz frequencies,” Sci. Rep. 6(1), 22027 (2016).
[Crossref] [PubMed]

Y. Zhu, W. Yuan, Y. Yu, and P. Wang, “Robustly efficient superfocusing of immersion plasmonic lenses based on coupled nanoslits,” Plasmonics 11(6), 1543–1548 (2016).
[Crossref]

Y. Zhu, W. Yuan, Y. Yu, and J. Diao, “Metallic planar lens formed by coupled width-variable nanoslits for superfocusing,” Opt. Express 23(15), 20124–20131 (2015).
[Crossref] [PubMed]

Zhuang, S.

L. Chen, Y. Wei, X. Zang, Y. Zhu, and S. Zhuang, “Excitation of dark multipolar plasmonic resonances at terahertz frequencies,” Sci. Rep. 6(1), 22027 (2016).
[Crossref] [PubMed]

Appl. Phys. Lett. (2)

B. Jia, H. Shi, J. Li, Y. Fu, C. Du, and M. Gu, “Near-field visualization of focal depth modulation by step corrugated plasmonic slits,” Appl. Phys. Lett. 94(15), 151912 (2009).
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[Crossref]

J. Opt. A, Pure Appl. Opt. (1)

W. L. Barnes, “Surface plasmon–polariton length scales: a route to sub-wavelength optics,” J. Opt. A, Pure Appl. Opt. 8(4), S87–S93 (2006).
[Crossref]

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K. Huang, H. Ye, J. Teng, S. P. Yeo, B. Luk’yanchuk, and C.-W. Qiu, “Optimization-free superoscillatory lens using phase and amplitude masks,” Laser Photonics Rev. 8(1), 152–157 (2014).
[Crossref]

Light Sci. Appl. (1)

X. Ni, S. Ishii, A. V. Kildishev, and V. M. Shalaev, “Ultra-thin, planar, Babinet-inverted plasmonic metalenses,” Light Sci. Appl. 2(4), e72 (2013).
[Crossref]

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L. Lin, X. M. Goh, L. P. McGuinness, and A. Roberts, “Plasmonic lenses formed by two-dimensional nanometric cross-shaped aperture arrays for Fresnel-region focusing,” Nano Lett. 10(5), 1936–1940 (2010).
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H. Gao, J. K. Hyun, M. H. Lee, J.-C. Yang, L. J. Lauhon, and T. W. Odom, “Broadband plasmonic microlenses based on patches of nanoholes,” Nano Lett. 10(10), 4111–4116 (2010).
[Crossref] [PubMed]

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9(1), 235–238 (2009).
[Crossref] [PubMed]

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W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

Opt. Express (6)

Opt. Lett. (1)

Phys. Rev. B (1)

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73(3), 035407 (2006).
[Crossref]

Plasmonics (4)

Z. Shi, Y. Fu, X. Zhou, and S. Zhu, “Polarization effect on superfocusing of a plasmonic lens structured with radialized and chirped elliptical nanopinholes,” Plasmonics 5(2), 175–182 (2010).
[Crossref]

J. Ji, Y. Meng, L. Sun, X. Wu, and J. Wang, “Strong focusing of plasmonic lens with nanofinger and multiple concentric rings under radially polarized illumination,” Plasmonics 11(1), 23–27 (2016).
[Crossref]

Y. Zhu, W. Yuan, Y. Yu, and P. Wang, “Robustly efficient superfocusing of immersion plasmonic lenses based on coupled nanoslits,” Plasmonics 11(6), 1543–1548 (2016).
[Crossref]

H. Shao, J. Wang, D. Liu, Z.-D. Hu, X. Xia, and T. Sang, “Plasmonic planar lens based on slanted nanoslit array,” Plasmonics 12(2), 361–367 (2017).
[Crossref]

Sci. Rep. (1)

L. Chen, Y. Wei, X. Zang, Y. Zhu, and S. Zhuang, “Excitation of dark multipolar plasmonic resonances at terahertz frequencies,” Sci. Rep. 6(1), 22027 (2016).
[Crossref] [PubMed]

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Figures (11)

Fig. 1
Fig. 1 Schematic illustration of structural parameters. (a) A double-turn waveguide. (b) A designed plasmonic lens based on the geometrical optics and the wavefront reconstruction theory.
Fig. 2
Fig. 2 (a) The Poynting vector in the waveguide with d = 150 nm, w = 30 nm. (b) The simulated magnetic field distribution of Re(Hz) out of a waveguide structure.
Fig. 3
Fig. 3 Phase delay caused by the parameters d and w, assuming t = w1 = w2 = w. The phase delay of double-turn waveguides displays an increasing trend as d increases and w decreases. The narrower the nanoslits, the greater influence of d on its phase delay.
Fig. 4
Fig. 4 The increase of phase delay in the double-turn waveguides is obvious compared to the nanoslits with the same width and depth, as the parameter d increases from 30 nm to 450 nm. The structural parameter w ranges from 10 nm to 50 nm. In the case of w = 30 nm and d = 400 nm, the phase delay of double-turn waveguide is about three times as large as that of nanoslit with 30 nm width on a 230nm-thick single-layer gold film.
Fig. 5
Fig. 5 Phase delay caused by the parameters d, t, w1 and w2. (a) The t ranges from 20 nm to 40 nm, assuming w1 = w2 = 30 nm. (b) The w2 ranges from 20 nm to 40 nm, assuming t = w1 = w = 30 nm. (c) The w1 ranges from 20 nm to 40 nm, assuming t = w2 = w = 30 nm. (d) The θ ranges from 0° to 60°, assuming t = w1 = w2 = w = 30 nm.
Fig. 6
Fig. 6 The magnetic field intensity in double-turn waveguide with different structural parameter θ, (a) θ = 0°, (b) θ = 15°, (c) θ = 30°, (d) θ = 45°, (e) θ = 60°.The structural parameters t = w1 = w2 = w = 30 nm and d = 400 nm remain constant for all the cases.
Fig. 7
Fig. 7 The FDTD simulation results of the metallic planar lens for the focal length f = 1 µm under the assumption of t = w1 = w2 = w = 30 nm. (a) The half geometry of the lens composed of double-turn waveguides (yellow). (b) The FDTD simulation result of the magnetic field intensity. (c) The derived |Hz|2 at the focal plane.
Fig. 8
Fig. 8 The focusing performance of the plasmonic lenses with different film thicknesses. The simulated magnetic field intensity for (a) the original lens with t1 = 100 nm, (b) the adjusted lens with t1 = 75 nm, (c) the adjusted lens with t1 = 50 nm. In all cases, t2 keeps a constant value of 100 nm. The insets show the corresponding field intensity distribution at the focal plane. The white dashed lines express the exit surfaces of the lenses.
Fig. 9
Fig. 9 The focusing performance of the plasmonic lenses with different film thicknesses. The simulated magnetic field intensity for (a) the original lens with t2 = 100 nm, (b) the adjusted lens with t2 = 75 nm, (c) the adjusted lens with t2 = 50 nm. In all cases, t1 keeps a constant value of 100 nm. The insets show the corresponding field intensity distribution at the focal plane. The white dashed lines express the exit surfaces of the lenses.
Fig. 10
Fig. 10 The focusing performance of the plasmonic lenses with different slit widths. The simulated magnetic field intensity for (a) the adjusted lens with w1 = 20 nm, (b) the original lens with w1 = 30 nm, (c) the adjusted lens with w1 = 40 nm. In all cases, w2 keeps a constant value of 30 nm. The insets show the corresponding field intensity distribution at the focal plane. The white dashed lines express the exit surfaces of the lenses.
Fig. 11
Fig. 11 The focusing performance of the plasmonic lenses with different slit width The simulated magnetic field intensity for (a) the adjusted lens with w2 = 20 nm, (b) the original lens with w2 = 30 nm, (c) the adjusted lens with w2 = 40 nm. In all cases, w1 keeps a constant value of 30 nm. The insets show the corresponding field intensity distribution at the focal plane. The white dashed lines express the exit surfaces of the lenses.

Tables (2)

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Table 1 Structural parameters for the designed plasmonic lens with a focal length f = 1 μm

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Table 2 The aspect ratio and deviation of the focal length between the theoretical design, numerical simulation, and experimental measurement (unit: μm)

Equations (5)

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tanh( k 1 w 2 )=- ε d k 2 ε m k 1 .
δ m = 1 k 0 | ε m ' + ε d ε m ' 2 | 1 2 .
φ(y)=2nπ+ 2π λ - 2π f 2 + y 2 λ .
r R = 0.61λ NA .
NA=nsinα.

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